Topological Entropy of a Graph Map

被引：0

作者：

Tai Xiang SUN ^{[1
]}

机构：

[1] Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi University of Finance and Economics

来源：

Acta Mathematica Sinica,English Series | 2018年 / 02期

关键词：

Topological entropy; periodic point; ω-limit set; recurrent point;

D O I：

暂无

中图分类号：

O157.5 [图论];

学科分类号：

070104 ;

摘要：

Let G be a graph and f : G → G be a continuous map. Denote by h(f), P(f), AP(f), R(f)and ω(x, f) the topological entropy of f, the set of periodic points of f, the set of almost periodic points of f, the set of recurrent points of f and the ω-limit set of x under f, respectively. In this paper,we show that the following statements are equivalent:(1) h(f) > 0.(2) There exists an x ∈ G such that ω(x, f) ∩ P(f) = ? and ω(x, f) is an infinite set.(3) There exists an x ∈ G such that ω(x, f)contains two minimal sets.(4) There exist x, y ∈ G such that ω(x, f)-ω(y, f) is an uncountable set and ω(y, f) ∩ω(x, f) = ?.(5) There exist an x ∈ G and a closed subset A ? ω(x, f) with f(A) ? A such that ω(x, f)-A is an uncountable set.(6) R(f)-AP(f) = ?.(7) f |P(f)is not pointwise equicontinuous.

引用

页码：194 / 208

页数：15